The Cluster Algorithms for Solving Problems with Asymmetric Proximity Measures

Cluster analysis is used in various scientific and applied fields and is a topical subject of research. In contrast to the existing methods, the algorithms offered in this paper are intended for clustering objects described by feature vectors in a space in which the symmetry axiom is not satisfied....

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Bibliographic Details
Published in:Numerical analysis and applications Vol. 11; no. 2; pp. 99 - 107
Main Authors: Aidinyan, A. R., Tsvetkova, O. L.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.04.2018
Springer Nature B.V
Subjects:
Algorithms
Cluster analysis
Clustering
Criteria
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Vectors (mathematics)
clustering
cluster analysis
clustering algorithms
the axiom of symmetry
asymmetric proximitymeasure
ISSN:1995-4239, 1995-4247
Online Access:Get full text
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Summary:Cluster analysis is used in various scientific and applied fields and is a topical subject of research. In contrast to the existing methods, the algorithms offered in this paper are intended for clustering objects described by feature vectors in a space in which the symmetry axiom is not satisfied. In this case, the clustering problem is solved using an asymmetric proximity measure. The essence of the first of the proposed clustering algorithms consists in sequential generation of clusters with simultaneous transfer of the objects clustered from previously created clusters into a current cluster if this reduces the quality criterion. In comparison with the existing algorithms of non-hierarchical clustering, such an approach to cluster generation makes it possible to reduce the computational costs. The second algorithmis a modified version of the first one andmakes it possible to reassign the main objects of clusters to further decrease the value of the proposed quality criterion.
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ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423918020015